Simplify the following expression: $k = \dfrac{-8p^2 - 32p + 96}{p - 2} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-8$ , so we can rewrite the expression: $ k =\dfrac{-8(p^2 + 4p - 12)}{p - 2} $ Then we factor the remaining polynomial: $p^2 + {4}p {-12} $ ${-2} + {6} = {4}$ ${-2} \times {6} = {-12}$ $ (p {-2}) (p + {6}) $ This gives us a factored expression: $\dfrac{-8(p {-2}) (p + {6})}{p - 2}$ We can divide the numerator and denominator by $(p + 2)$ on condition that $p \neq 2$ Therefore $k = -8(p + 6); p \neq 2$